Question

A falling brick has a mass of 1.5 kg and is moving straight downward with a speed of 5.0 m/s. A 1.5-kg physics book is sliding across the floor with a speed of 5.0 m/s. A 1.5-kg melon is traveling with a horizontal velocity component 3.0 m/s to the right and a vertical component 4.0 m/s upward. Do all of these objects have the same velocity? Do all of them have the same kinetic energy? For both questions, give your reasoning.

Short answer

The velocities are not same, and the kinetic energy will be same.

Step-by-step solution

Describe the Kinetic Energy

The expression for the Kinetic Energy is given by,

$\mathit{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

Here, mis the mass of an object, and v is the velocity of the object.

Determine whether all of the objects have the same velocity and kinetic energy

The brick is moving in a downward direction. The velocity of the brick is .

$\left({\overrightarrow{v}}_b\right)=-5.0\mathrm{m}/\mathrm{s}$

The velocity of the physics book is $\left({\overrightarrow{v}}_b\right)=-5.0\mathrm{m}/\mathrm{s}$.

The velocity of the melon is $\left({\overrightarrow{v}}_m\right)=3.0\hat{i}+4.0\hat{j}$. Here,$\hat{i}$ , and$\hat{j}$ are unit vectors along the horizontal and vertical direction respectively.

The magnitude of the velocity is,

$$\begin{gathered} \left|{\overrightarrow{v}}_m\right|=\sqrt{{\left(3\right)}^2+{\left(4\right)}^2} \\ =\sqrt{25} \\ =5\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore, the velocities are not the same.

Calculate the kinetic energy of the brick.

$$\begin{gathered} K_b=\frac{1}{2}m{v}_b^2 \\ =\frac{1}{2}\left(1.5\mathrm{kg}\right){\left(-5\mathrm{m}/\mathrm{s}\right)}^2 \\ =18.75\mathrm{J} \end{gathered}$$

Calculate the kinetic energy of the physics book.

$$\begin{gathered} K_p=\frac{1}{2}m{v}_p^2 \\ =\frac{1}{2}\left(1.5\mathrm{kg}\right){\left(5\mathrm{m}/\mathrm{s}\right)}^2 \\ =18.75\mathrm{J} \end{gathered}$$

Calculate the kinetic energy of the melon.

$$\begin{gathered} K_m=\frac{1}{2}m{v}_m^2 \\ =\frac{1}{2}\left(1.5\mathrm{kg}\right){\left(5\mathrm{m}/\mathrm{s}\right)}^2 \\ =18.75\mathrm{J} \end{gathered}$$

Therefore, the kinetic energy of all bodies are the same.